As one of the most luminous Cepheids in the Milky Way, the 41.5-day RS Puppis is an analog of the long-period Cepheids used to measure extragalactic distances. An accurate distance to this star would therefore help anchor the zero-point of the bright end of the period-luminosity relation. But, at a distance of about 2 kpc, RS Pup is too far away for measuring a direct trigonometric parallax with a precision of a few percent with existing instrumentation. RS Pup is unique in being surrounded by a reflection nebula, whose brightness varies as pulses of light from the Cepheid propagate outwards. We present new polarimetric imaging of the nebula obtained with HST/ACS. The derived map of the degree of linear polarization pL allows us to reconstruct the three-dimensional structure of the dust distribution. To retrieve the scattering angle from the pL value, we consider two different polarization models, one based on a Milky Way dust mixture and one assuming Rayleigh scattering. Considering the derived dust distribution in the nebula, we adjust a model of the phase lag of the photometric variations over selected nebular features to retrieve the distance of RS Pup. We obtain a distance of 1910 +/- 80 pc (4.2%), corresponding to a parallax of 0.524 +/- 0.022 mas. The agreement between the two polarization models we considered is good, but the final uncertainty is dominated by systematics in the adopted model parameters. The distance we obtain is consistent with existing measurements from the literature, but light echoes provide a distance estimate that is not subject to the same systematic uncertainties as other estimators (e.g. the Baade-Wesselink technique). RS Pup therefore provides an important fiducial for the calibration of systematic uncertainties of the long-period Cepheid distance scale.
The distance to pulsating stars is classically estimated using the parallax-of-pulsation (PoP) method, which combines spectroscopic radial velocity measurements and angular diameter estimates to derive the distance of the star. An important application of this method is the determination of Cepheid distances, in view of the calibration of their distance scale. However, the conversion of radial to pulsational velocities in the PoP method relies on a poorly calibrated parameter, the projection factor (p-factor). We aim to measure empirically the value of the p-factors of a homogeneous sample of nine Galactic Cepheids for which trigonometric parallaxes were measured with the Hubble Space Telescope Fine Guidance Sensor. We use the SPIPS algorithm, a robust implementation of the PoP method that combines photometry, interferometry, and radial velocity measurements in a global modeling of the pulsation. We obtained new interferometric angular diameters using the PIONIER instrument at the Very Large Telescope Interferometer, completed by data from the literature. Using the known distance as an input, we derive the value of the p-factor and study its dependence with the pulsation period. We find the following p-factors: 1.20 $\pm$ 0.12 for RT Aur, 1.48 $\pm$ 0.18 for T Vul, 1.14 $\pm$ 0.10 for FF Aql, 1.31 $\pm$ 0.19 for Y Sgr, 1.39 $\pm$ 0.09 for X Sgr, 1.35 $\pm$ 0.13 for W Sgr, 1.36 $\pm$ 0.08 for $\beta$ Dor, 1.41 $\pm$ 0.10 for $\zeta$ Gem, and 1.23 $\pm$ 0.12 for $\ell$ Car. These values are consistently close to p = 1.324 $\pm$ 0.024. We observe some dispersion around this average value, but the observed distribution is statistically consistent with a constant value of the p-factor as a function of the pulsation period. The error budget of our determination of the p-factor values is presently dominated by the uncertainty on the parallax, a limitation that will soon be waived by Gaia.
Les Cepheides sont utilisees depuis plus d’un siecle comme chandelles cosmiques pour estimer des distances dans l’univers, grâce a la relation qui unie leur periode de pulsation et leur luminosite absolue. La calibration de cette relation (dite Loi de Leavitt, en hommage a sa decouvreuse) repose sur des estimations independantes de distances, qui sont generalement realisees grâce a la methode de la parallaxe de pulsation. Cette technique assez simple repose sur la comparaison de la variation de diametre angulaire (mesuree par exemple via des relations de brillance de surface) et de la variation de diametre lineaire (obtenue apres une simple integration de la courbe de vitesse radiale). Durant ma these j’ai fait usage d’une implementation novatrice de cette methode : le code SPIPS developpe par Antoine Merand. Celui-ci permet un ajustement simultane de toutes les observables disponibles (photometrie multi-filtre et multi-bande, vitesses radiales, diametres interferometriques et temperatures effectives), se traduisant par une meilleur precision statistique. Le code integre egalement des modeles d’atmosphere permettant de prendre en compte la physique des Cepheides, et d’assurer un meilleur controle des systematiques (par exemple, la presence d’une enveloppe circumstellaire se traduit par un exces apparent de la magnitude infrarouge). Bien que precise et elegante, cette methode ne permet de mesurer des distances qu’a un parametre pres, le facteur de projection p utilise pour convertir la vitesse radiale (deduite de la spectroscopie) en vitesse de pulsation. La valeur de p et sa dependance avec la periode de pulsation sont encore largement debattues. Pour les rares Cepheides dont la distance est connue avec une precision suffisante (par exemple grâce a une mesure de parallaxe), il est possible de faire un usage inverse de la methode SPIPS et de remonter a la valeur de p, et c’est ce que j’ai fait durant ma these. Grâce a cette methode, j’ai tout d’abord calcule le p-facteur de la Cepheide de type II κ Pavonis, pour laquelle nous aboutissons a p = 1.26 ± 0.07. J’ai ensuite etendu mon etude a un plus grand echantillon de Cepheides galactiques de parallaxe connue, auxquelles j’ai ajoute RS Pup, celebre pour ses echos de lumiere. Contrairement aux predictions de certains auteurs, l’etude globale de ces etoiles a permis de conclure a une dependance plutot faible de p en fonction de la periode. De fait, nous proposons pour le moment d’utiliser une valeur constante moyenne de p = 1.326 ± 0.021. Dans l’etat de l’art actuel, la precision n’est pas limitee par la methode, mais par les mesures de distance elles-memes. L’arrivee des parallaxes a moins de 1% du satellite Gaia permettra sans doute une avancee rapide dans cette problematique, ce travail preliminaire ayant dores et deja permis de demontrer la faisabilite de la methode et d’aboutir a des resultats prometteurs.
The parallax of pulsation, and its implementations such as the Baade-Wesselink method and the infrared surface bright- ness technique, is an elegant method to determine distances of pulsating stars in a quasi-geometrical way. However, these classical implementations in general only use a subset of the available observational data. Freedman & Madore (2010) suggested a more physical approach in the implementation of the parallax of pulsation in order to treat all available data. We present a global and model-based parallax-of-pulsation method that enables including any type of observational data in a consistent model fit, the SpectroPhoto-Interferometric modeling of Pulsating Stars (SPIPS). We implemented a simple model consisting of a pulsating sphere with a varying effective temperature and a combina- tion of atmospheric model grids to globally fit radial velocities, spectroscopic data, and interferometric angular diameters. We also parametrized (and adjusted) the reddening and the contribution of the circumstellar envelopes in the near-infrared photometric and interferometric measurements. We show the successful application of the method to two stars: delta Cep and eta Aql. The agreement of all data fitted by a single model confirms the validity of the method. Derived parameters are compatible with publish values, but with a higher level of confidence. The SPIPS algorithm combines all the available observables (radial velocimetry, interferometry, and photometry) to estimate the physical parameters of the star (ratio distance/ p-factor, Teff, presence of infrared excess, color excess, etc). The statistical precision is improved (compared to other methods) thanks to the large number of data taken into account, the accuracy is improved by using consistent physical modeling and the reliability of the derived parameters is strengthened thanks to the redundancy in the data.
Aims. We aim at detecting and characterizing the main-sequence companion of the Cepheid AX Cir (P orb ~ 18 yrs). The long-term objective is to estimate the mass of both components and the distance to the system.Methods. We used the PIONIER combiner at the VLT Interferometer to obtain the first interferometric measurements of the short-period Cepheid AX Cir and its orbiting component.Results. The companion is resolved by PIONIER at a projected separation ρ = 29.2 ± 0.2 mas and projection angle PA = 167.6 ± 0.3°. We measured H -band flux ratios between the companion and the Cepheid of 0.90 ± 0.10% and 0.75 ± 0.17%, at pulsation phases for the Cepheid of φ = 0.24 and 0.48, respectively. The lower contrast at φ = 0.48 is due to the increased brightness of the Cepheid compared to φ = 0.24. This gives an average apparent magnitude m H (comp) = 9.06 ± 0.24 mag. The limb-darkened angular diameter of the Cepheid at the two pulsation phases was measured to be θ LD = 0.839 ± 0.023 mas and θ LD = 0.742 ± 0.020 mas, at φ = 0.24 and 0.48, respectively. A lower limit on the total mass of the system was also derived based on our measured separation, and we found M T ≥ 9.7 ± 0.6 M ⊙ .
As one of the most luminous Cepheids in the Milky Way, the 41.5-day RS Puppis is an analog of the long-period Cepheids used to measure extragalactic distances. An accurate distance to this star would therefore help anchor the zero-point of the bright end of the period-luminosity relation. But, at a distance of about 2 kpc, RS Pup is too far away for measuring a direct trigonometric parallax with a precision of a few percent with existing instrumentation. RS Pup is unique in being surrounded by a reflection nebula, whose brightness varies as pulses of light from the Cepheid propagate outwards. We present new polarimetric imaging of the nebula obtained with HST/ACS. The derived map of the degree of linear polarization pL allows us to reconstruct the three-dimensional structure of the dust distribution. To retrieve the scattering angle from the pL value, we consider two different polarization models, one based on a Milky Way dust mixture and one assuming Rayleigh scattering. Considering the derived dust distribution in the nebula, we adjust a model of the phase lag of the photometric variations over selected nebular features to retrieve the distance of RS Pup. We obtain a distance of 1910 +/- 80 pc (4.2%), corresponding to a parallax of 0.524 +/- 0.022 mas. The agreement between the two polarization models we considered is good, but the final uncertainty is dominated by systematics in the adopted model parameters. The distance we obtain is consistent with existing measurements from the literature, but light echoes provide a distance estimate that is not subject to the same systematic uncertainties as other estimators (e.g. the Baade-Wesselink technique). RS Pup therefore provides an important fiducial for the calibration of systematic uncertainties of the long-period Cepheid distance scale.
Abstract Cepheids are one of the most famous standard candles used to calibrate the Galactic distance scale. However, it is fundamental to develop and test independent tools to measure their distances, in order to reach a better calibration of their period-luminosity (P-L) relationship. We present here the first results obtained with the Integrated Parallax of Pulsation (IPoP) method, an extension of the classical Baade-Wesselink method that derives the distance by making a global modelisation of all the available data. With this method we aim to reach a 2% accuracy on distance measurements. Cepheid masses are also an essential key for our comprehension of those objects. We briefly present an original approach to derive observational constraint on Cepheid masses. Unfortunately, it does not lead to promising results.
Context. The distance to pulsating stars is classically estimated using the parallax-of-pulsation (PoP) method, which combines spectroscopic radial velocity (RV) measurements and angular diameter (AD) estimates to derive the distance of the star. A particularly important application of this method is the determination of Cepheid distances in view of the calibration of their distance scale. However, the conversion of radial to pulsational velocities in the PoP method relies on a poorly calibrated parameter, the projection factor (p -factor).Aims. We aim to measure empirically the value of the p -factors of a homogeneous sample of nine bright Galactic Cepheids for which trigonometric parallaxes were measured with the Hubble Space Telescope (HST) Fine Guidance Sensor.Methods. We use the SPIPS algorithm, a robust implementation of the PoP method that combines photometry, interferometry, and radial velocity measurements in a global modeling of the pulsation of the star. We obtained new interferometric angular diameter measurements using the PIONIER instrument at the Very Large Telescope Interferometer (VLTI), completed by data from the literature. Using the known distance as an input, we derive the value of the p -factor of the nine stars of our sample and study its dependence with the pulsation period.Results. We find the following p -factors: p = 1.20 ± 0.12 for RT Aur, p = 1.48 ± 0.18 for T Vul, p = 1.14 ± 0.10 for FF Aql, p = 1.31 ± 0.19 for Y Sgr, p = 1.39 ± 0.09 for X Sgr, p = 1.35 ± 0.13 for W Sgr, p = 1.36 ± 0.08 for β Dor, p = 1.41 ± 0.10 for ζ Gem, and p = 1.23 ± 0.12 for l Car.Conclusions. The values of the p -factors that we obtain are consistently close to p = 1.324 ± 0.024. We observe some dispersion around this average value, but the observed distribution is statistically consistent with a constant value of the p -factor as a function of the pulsation period (χ 2 = 0.669). The error budget of our determination of the p -factor values is presently dominated by the uncertainty on the parallax, a limitation that will soon be waived by Gaia .
Long-baseline interferometry is an important technique to spatially resolve binary or multiple systems in close orbits. By combining several telescopes together and spectrally dispersing the light, it is possible to detect faint components around bright stars. Aims. We provide a rigorous and detailed method to search for high-contrast companions around stars, determine the detection level, and estimate the dynamic range from interferometric observations. We developed the code CANDID (Companion Analysis and Non-Detection in Interferometric Data), a set of Python tools that allows us to search systematically for point-source, high-contrast companions and estimate the detection limit. The search pro- cedure is made on a N x N grid of fit, whose minimum needed resolution is estimated a posteriori. It includes a tool to estimate the detection level of the companion in the number of sigmas. The code CANDID also incorporates a robust method to set a 3σ detection limit on the flux ratio, which is based on an analytical injection of a fake companion at each point in the grid. We used CANDID to search for the companions around the binary Cepheids V1334 Cyg, AX Cir, RT Aur, AW Per, SU Cas, and T Vul. First, we showed that our previous discoveries of the components orbiting V1334 Cyg and AX Cir were detected at > 13 sigmas. The companion around AW Per is detected at more than 15 sigmas with a flux ratio of f = 1.22 +/- 0.30 %. We made a possible detection of the companion orbiting RT Aur with f = 0.22 +/- 0.11 %. It was detected at 3.8σ using the closure phases only, and so more observations are needed to confirm the detection. We also set the detection limit for possible undetected companions. We found that there is no companion with a spectral type earlier than B7V, A5V, F0V, B9V, A0V, and B9V orbiting V1334 Cyg, AX Cir, RT Aur, AW Per, SU Cas, and T Vul, respectively.
